{"paper":{"title":"Eigenvalue distribution analysis of multidimensional prolate matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Azita Mayeli, Jonathan Jaimangal, Luis Gomez, Tasfia Proma","submitted_at":"2025-07-14T15:55:07Z","abstract_excerpt":"We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it enables a rigorous study of joint time-frequency localization in higher dimensions. To achieve this, we define multidimensional time-limiting and frequency-limiting matrices tailored to signals on a Cartesian grid and construct a multi-indexed prolate matrix. We prove that the spectrum of this matrix exhibits an eigenvalue concentration phenomenon: the bulk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10412","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.10412/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}